Up to now, there have been a large number of publications regarding a reference voltage circuit which demonstrates a temperature independent characteristic by canceling a temperature dependent characteristic and which outputs a reference voltage of the order of 1.2 V.
First, the operation of a conventional reference voltage circuit is explained.
FIG. 10 shows an example of a conventional CMOS (Complementary MOS) reference voltage circuit. The reference voltage is obtained by inserting a resistor in a current loop of a reference current circuit which is termed a PTAT (Proportional to Absolute Temperature) current source circuit since in general the reference current circuit outputs the current proportional to temperature.
In FIG. 10, it is assumed that a transistor Q1 is a unit transistor and that the emitter area of a transistor Q2 is K1 times that of the unit transistor(K1>1).
If the base width modulation is neglected, the relationship between the collector current IC to the base-to-emitter voltage VBE of a transistor is given by:IC=K·ISexp(VBE/VT)  (1)where IS is the saturation current of a unit transistor and VT is the thermal voltage, which is given by:VT=kT/qwhere q is the magnitude of the unit electron charge,                k is Boltzmann's constant,        T is absolute temperature in kelvins, and        K is the emitter area ratio referenced to the unit transistor.        
Assuming that the DC current amplification factor of a transistor is sufficiently close to 1, and the base current is neglected, we shall find the following relationships:VBE1=VT ln {IC1/IS}  (2)VBE2=VT ln(IC2/(K1·IS))  (3)VBE1=VBE2+R1·IC2  (4)where ln {} is a logarithmic function.
By solving the equation (2) to (4), we obtainVT ln {K1·IC1/IC2}=R1·IC2  (5)
It is noted that, since transistors Q1 and Q2 controls the common gate voltage of transistors M3 and M4 through an operational amplifier 20 so that the equation (4) will be held valid, the transistors Q1 and Q2 are self-biased, and hence the drain currents ID3 and ID4 of the transistors M3 and M4 are equal to each other andID3=ID4=IC1=IC2  (6)
From the equation (5), we shall therefore have the following equation:ID3=ID4=IC1=IC2VT ln(K1)/R1  (7)
The drain current ID3 of the transistor M3 is converted by the resistor R2 to a voltage and becomes the reference voltage VREF. That is, the reference voltage VREF is expressed as follow.VREF=VBE1+R2·ID3=VBE1+R2·VT ln(K1)/R1  (8)
In the equation (8), the base-to-emitter voltage VBE1 of the transistor Q1, which is driven by the PTAT reference current, has a negative temperature characteristic on the order of approximately −1.9 mV/° C., which is slightly less than −2 mV, while the thermal voltage VT has a positive temperature characteristic of 0.0853 mV/° C.
Accordingly, in order that the output reference voltage VREF will not exhibit a temperature dependent characteristic, the cancellation of temperature dependency of the output reference voltage VREF may be performed by a combination of a voltage exhibiting a positive temperature characteristic and a voltage exhibiting a negative temperature characteristic.
That is, the value of (R2/R1)ln(K1) is 22.3, while that of (R2/R1)VT ln(K1) is 0.57V.
If the base-to-emitter voltage VBE1 is 0.7 V,{VBE1+(R2/R1)VT ln(K1)}=1.27V